It sounds like your husband was rear-ended by another vehicle while he was stopped at a red light. In most instances of a person being hit from behind it is usually evident who is at fault, even without witnesses. Your husband hopefully called the police who then would have written up a report which likely included exactly how the cars were situated after the accident.

Another party that investigates to determine who is at fault is the insurance company that the claim is put against. Their claims adjuster will take statements from both parties and look at the police report so they can determine who they find at fault and what they should payout.

Function of an Insurance Adjuster is an article you might find of interest.